All Questions
Tagged with classical-mechanics noethers-theorem
117
questions
0
votes
4
answers
374
views
Is Feynman correct when he suggests that Noether's Theorem requires quantum mechanics?
I'm reading the Feynman lectures on physics. In 52-3 he discusses how for each of the rules of symmetry there is a corresponding conservation law. I'm assuming he is referring to Noether's Theorem, ...
- 39
1
vote
0
answers
195
views
Dynamics of particles and fields on the torus: references
In some situations (e.g. molecular dynamics situations, Euclidean QFT, cosmology), a common trick to eliminate boundary effects or to provide an infrared cutoff is to use periodic boundary conditions. ...
5
votes
2
answers
775
views
Intuition behind the definition of Continuous Symmetry of a Lagrangian (Proof of Noether's Theorem)
Suppose there is a one-parameter family of continuous transformations that maps co-ordinates $q(t)\rightarrow Q(s,t)$ where the $s$ is the continuous parameter. Also, for when $s=0$ the transformation ...
- 2,958
1
vote
1
answer
179
views
Goldstein's derivation of Noether's theorem
This is a followup to my previoucs question: Translation invariance Noether's equation
In Goldstein's derivation of the Noether's theorem in chapter 13,
we have the infinitesimal transformation $$...
- 789
0
votes
3
answers
633
views
Translation invariance Noether's equation
In chapter 13 of Goldstein's classical mechanics, on page 591 when talking about Noether's theorem, Goldstein says we need condition 3, which is
$$\tag{13.133} \int_{\Omega'}\mathcal{L}(\eta_\rho'(x^\...
- 789
0
votes
2
answers
85
views
How did Noether use the total time derivation to get her conservation of energy? [duplicate]
I was informed by @hft that by combining the total time derivation:
$$\frac{dL}{dt} = \frac{\partial L}{\partial x}\dot{x} +
\frac{\partial L}{\partial \dot{x}}\ddot{x} +
\frac{\partial L}{\partial t}$...
- 625
-1
votes
2
answers
620
views
Conservation theorem for cyclic coordinates in the Lagrangian
Suppose $q_1,q_2,...,q_j,..,q_n$ are the generalized coordinates of a system.
$q_j$ is not there in the Lagrangian (it is cyclic).
Then $\frac{\partial L}{\partial\dot q_j}=constant$
In Goldstein, it ...
- 293
1
vote
1
answer
73
views
Are there non time-symmetric systems that increase total energy over time?
According to Noether's theorem, systems that are not time-symmetric have $\frac{\mathrm{d}E}{\mathrm{d}t}\neq0$. I have essentially two questions, then:
Are there any real systems (discovered or ...
- 1,775
2
votes
3
answers
480
views
Lagrangian first integral
I want to extremize $$\int dt \frac{\sqrt{\dot x ^2 + \dot y ^2}}{y}.$$
I have thought that, since the Lagrangian $L(y, \dot y, \dot x)$ is $t$ dependent only implicitly, that i could use the fact ...
- 980
2
votes
3
answers
191
views
Noether‘s theorem: Why can function be dependent of $\dot{q}$?
We define a continuous symmetry in Lagrangian mechanics as follows:
$$\delta L\overset{!}{=}\epsilon\frac{\mathrm{d}}{\mathrm{d} t} f(q,\dot{q}, t)$$
Where $\epsilon\in\mathbb{R}$ is a parameter in ...
- 425
1
vote
0
answers
70
views
Symmetry of a time-dependent Lagrangian
How do I get the group of symmetries and the constant of motion of $L=\frac{\dot{x}^2}{2}m+V(x+ct)$ where c is a constant?
When I tried to solve it, it was to look for shifts in $x$ and $ct$ under ...
- 11
5
votes
6
answers
1k
views
How is energy conservation & Noether's theorem a non-trivial statement?
Noether's theorem says that energy conservation is a result of temporal translation symmetry of the laws of physics. This is implied to be - and I'm not saying it's not - a very non-trivial statement. ...
- 20.6k
4
votes
3
answers
269
views
Newtonian vs Lagrangian symmetry
Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the ...
- 1,795
17
votes
6
answers
3k
views
What symmetry is responsible for the amplitude independence of the period of a simple harmonic oscillator?
In the ICTP lectures of Y. Grossman: Standard Model 1, in about minute 54:00, he leaves an informal homework for the students. He ask to find the symmetry related to the conservation of the amplitude ...
- 5,568
1
vote
0
answers
188
views
Physical interpretation of the symmetry for the Runge-Lenz vector
In the post What symmetry causes the Runge-Lenz vector to be conserved?, and based on the results of https://arxiv.org/abs/1207.5001, it was it was discussed that the Runge-Lenz vector is the ...
- 3,915